How would you say "I care about you" in French, by which you mean to whom it is directed at that their well-being and happiness are of concern to you?

Specifically, I want to capture these types of situations:
- showing concern for a friend who has fallen into difficult circumstances
- a parent explaining to a child who feels alone and fears abandonment that everything's okay
- explaining to a lover that your gestures of affection come from a sincere place

I presume for the last, « je tiens à toi » is spot on. My French is poor so I am unable to appreciate the strength of the sentiment.

I feel "tu peux compter sur moi" as being slightly different, it introduces an idea of reliance, more than just concern, and I think it would better translate as "You can rely on me".
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LaureDec 19 '13 at 17:33

Yes, you're right. Still, I think I could say it in this particular context, but you are right to note the slightly different meaning, thanks!
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MBRDec 19 '13 at 17:36

In addition to "je tiens à toi", which would suit every case and that you can modulate with adverbs to suit the situation : "je tiens beaucoup à toi", "je tiens vraiment à toi", "je tiens très fort (vraiment très fort) à toi" ; you could use :

to a friend: "tu comptes beaucoup pour moi" ; "tu es un ami très cher",
to a child: "tu m'es très cher",
to a lover: the previous ones plus "je t'aime".Aimer is one of the received translations for the verb "care" outside a nursing
context. And the usual one when in a negative situation : "I don't much care for him/her" -> "je ne l'aime pas beaucoup".